Abstract: We discuss generic limits posed by the trap in atomic systems on the accuratedetermination of critical parameters for second-order phase transitions, fromwhich we deduce optimal protocols to extract them. We show that under currentexperimental conditions the in-situ density profiles are barely suitable for anaccurate study of critical points in the strongly correlated regime. Contraryto recent claims, the proper analysis of time-of-fight images yields criticalparameters accurately.